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Don Blasius

Publications and source records attributed to Don Blasius.

2 recordsLinked to original sources
arXiv2016

Complex conjugation and Shimura varieties

In this paper we study the action of complex conjugation on Shimura varieties and the problem of descending these to the maximal totally real field of the reflex field. We prove the existence of such descent for many Shimura varieties whose associated adjoint group has certain factors of type A or D. This includes a large family of Shimura varieties of abelian type. Our considerations and constructions are carried out purely at the level of Shimura data and group theory.

math.NT↗
arXiv2005

Hilbert Modular Forms and the Ramanujan Conjecture

This paper completes the proof of the Ramanujan Conjecture for holomorphic Hilbert modular forms whose weights are all congruent modulo 2. As a consequence, the Weight-Monodromy Conjecture and the zeta function conjecture of Langlands are verified for all Quaternionic Shimura varieties.

math.NT↗